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Considering potential attacks from cloud-computing and quantum-computing, it is becoming necessary to provide higher security elliptic curves. The hidden Markov models are introduced for designing the trace-vector computation algorithm to accelerate the search for elliptic curve (EC) base-points. We present a new algorithm for secure Koblitz EC generation based on evolutionary cryptography theory. The algorithm is tested by selecting a secure Koblitz EC over the field F(2 2000 ), withdoi:10.1007/s11432-012-4552-4 fatcat:qg55nmpnm5fjtf65rybqoefp3a